Question

Алгебраические дроби помогите! сложение и вычитание

Answer 1

Algebraic Fractions: Addition and Subtraction

Algebraic fractions involve the manipulation and simplification of expressions that contain variables in the numerator and/or denominator. In this response, we will discuss the concepts of addition and subtraction of algebraic fractions.

Addition of Algebraic Fractions: To add algebraic fractions, we need to have a common denominator. Here are the steps to follow:

1. Find the least common multiple (LCM) of the denominators. 2. Rewrite each fraction with the LCM as the new denominator. 3. Add the numerators together. 4. Simplify the resulting fraction, if possible.

Subtraction of Algebraic Fractions: Subtraction of algebraic fractions follows a similar process to addition. The steps are as follows:

1. Find the least common multiple (LCM) of the denominators. 2. Rewrite each fraction with the LCM as the new denominator. 3. Subtract the numerators. 4. Simplify the resulting fraction, if possible.

Let's look at some examples to illustrate these concepts.

Example 1: Addition Consider the addition of the fractions 1/3 and 1/5.

1. The LCM of 3 and 5 is 15. 2. Rewrite each fraction with 15 as the denominator: 5/15 and 3/15. 3. Add the numerators: 5/15 + 3/15 = 8/15. 4. The resulting fraction, 8/15, is already in its simplest form.

Example 2: Subtraction Let's subtract the fractions 2/7 and 1/4.

1. The LCM of 7 and 4 is 28. 2. Rewrite each fraction with 28 as the denominator: 8/28 and 7/28. 3. Subtract the numerators: 8/28 - 7/28 = 1/28. 4. The resulting fraction, 1/28, is already in its simplest form.

Remember to always simplify the resulting fraction if possible.

I hope this explanation helps! If you have any further questions, please feel free to ask.